(And now a word from our resident contrarian

)
Fly lines are a consumable product. Check for cracks, especially around 15 to 25 feet from the tip. Once the coating is cracked or split anywhere, the line is toast. Most modern fly line coatings (not the core) are made from PVC. A few are Urethane. PVC fly lines go bad goes bad from the plasticizer leaching out over time. PVC is stiff and inflexible without plasticizer. Plasticizer loss is what leads to cracking. UV exposure is the main enemy, but heat can contribute too (I am not sure how much heat is damaging, but I wouldn't store my fly lines in a hot car trunk for a long period, as wfjord has mentioned).
Overstretching the line does not help for longevity, so try not to hook too many big fish

Cleaning the fly line by running it through a soft towel wetted with a a small amount of dish soap and water is not a bad idea. Rinse and air dry. Just the way Don did it.
Fly line treatments can theoretically add a slick coating to make the line shoot faster through the guides, help the fly line float slightly better by making the surface a bit more water repellent, and protect against further UV damage. If none of these matter for your situation, then you don't need a line treatment.
A treatment won't introduce new plasticizer. Some fly line treatments will attract dirt in hotter climates. Best to avoid treatments that leave a wet or oily feel behind, like Amour-all or organic oils and fats.
The fly line makers are most likely reselling a vinyl treatment product, but they won't tell us what it is so they can sell a tiny bottle for triple the price. If you want to use a general purpose product that has been rumored to also be used by some of the fly line companies and is popular with lots of fly fishermen, take a look at Aerospace 303 Marine. Good for the vinyl on your boat too!
Scientific Angler has these little cleaning/buffing pads that are slightly abrasive. If I feel like carrying more junk with me, I will carry one of these and use on the water if the line is getting grimy. In addition to removing grime, they smooth out any small scratches.
I rarely use line treatments nowadays, but I am more of a minimalist than most. I wash my lines when they get too dirty. I have worn the cork grips out on rods from extended use, but have yet to damage a guide from abrasion.
-J